We prove a general possibility result for collective decision problems where individual allocations are one-dimensional, preferences are single-peaked (strictly convex), and feasible allocation profiles cover a closed convex set. Special cases include the celebrated median voter theorem (Black...

This paper investigates one of the possible weakening of the (too demanding) assumptions of the Gibbard-Satterthwaite theorem. Namely we deal with a class of voting schemes where at the same time the domain of possible preference preordering of any agent is limited to single-peaked preferences,...